I. Alpha-synuclein interaction with VDAC as a mechanism of mitochondrial regulation and toxicity in Parkinson disease Emerging evidence establishes the critical role of mitochondria in the pathogenesis of neurodegenerative diseases including Parkinsons (PD) and Alzheimers disease. Dysfunction of mitochondrial enzyme complexes, impaired oxidative phosphorylation, increased production of reactive oxygen species, mitochondrial outer membrane permeabilization, enhanced apoptosis, and morphological alterations of mitochondria have been associated with these pathologies. Neurons are especially sensitive to mitochondrial dysfunction because of their high demand for energy and their characteristic subcellular distribution of mitochondria. Participation of the small, intrinsically disordered protein alpha-synuclein (a-syn) in PD pathogenesis has been well documented. Although recent research demonstrates the involvement of a-syn in mitochondrial dysfunction in neurodegeneration and suggests direct interaction of a-syn with mitochondria, the molecular mechanism(s) of a-syn toxicity and its effect on neuronal mitochondria remain vague. Using channel reconstitution technique we have found that at nanomolar concentrations, a-syn reversibly blocks VDAC, the major transport pore of the mitochondrial outer membrane that controls most of the metabolite fluxes in and out of the mitochondria. It is clear that any restriction of metabolite exchange through VDAC may lead to disturbance of the mitochondrial energetic function and therefore, to cell metabolism dysfunction. Moreover, through the detailed analysis of the blockage kinetics we came to the conclusion that a-syn is able to translocate through the channel. Implication of VDAC in regulation of a-syn entrance into mitochondria may be of an immediate importance for the understanding of mitochondrial dysfunctions in PD. Indeed, after reaching the intermembrane space, a-syn may target complexes of the mitochondrial respiratory chain in the inner mitochondrial membrane. Thus, our results suggest that depending on the physiological conditions, a-syn interaction with VDAC could be involved in regulation of normal mitochondrial respiration, in a-syn-induced mitochondrial dysfunction, or both. Supporting our in vitro experiments, a yeast model of PD showed that a-syn toxicity in yeast depends on VDAC, demonstrating a-syn interaction with VDAC in living cells. The functional interactions between VDAC and a-syn, revealed by the present study, point toward the long sought after physiological and pathophysiological roles for monomeric a-syn in PD and in other a-synucleinopathies and for the first time suggest a pathway for a-syn across the mitochondrial outer membrane. We believe that these results are able to reconcile a number of previous conflicting observations of various a-syn effects on mitochondrial bioenergetics. II. Complexity of voltage gating of beta-barrel channels The functional role of voltage gating, that is, voltage-sensitive transitions of VDAC between its open and closed states, is in regulation of both ATP delivery to the cytosol and ADP access to the electron transport chain complexes in the mitochondrial inner membrane. According to this line of reasoning, VDAC closure limits mitochondrial oxidative phosphorylation whereas VDAC opening favors it. VDAC gating is remarkably complex. Nevertheless, its reproducible dependence on such environmental conditions as pH, osmotic pressure, presence of poly-anions, and membrane lipid content among others has been reported, which necessitates some means of their empirical quantitative characterization. Channel conformation sensitivity to the applied transmembrane voltage manifests itself in conductance hysteresis which is observed when the voltage is periodically varied with time. The objective of our study was to examine VDAC conductance hysteresis in a wide frequency range in an attempt to reconcile the recognized complexity of VDAC gating with the simplicity of its well-accepted characterization in terms of a two-state equilibrium model for the opening branches of the hysteresis curves. Although this phenomenon has been used in studies of VDAC gating for nearly four decades, full hysteresis curves have never been reported, because the focus was solely on the opening branches of the hysteresis loops. We studied the hysteretic response of a multichannel VDAC system in a planar bilayer to a triangular voltage ramp the frequency of which was varied over nearly three orders of magnitude, from 0.5 mHz to 0.2 Hz. We found that in this wide frequency range the area encircled by the hysteresis curves changes by less than a factor of three, suggesting broad distribution of the characteristic times and strongly non-equilibrium behavior. At the same time, quasi-equilibrium two-state behavior was observed for the hysteresis branches corresponding to VDAC opening. This enables calculation of the usual equilibrium gating parameters, gating charge and voltage of equipartitioning, which were found to be almost insensitive to the ramp frequency. To rationalize this peculiarity, we hypothesize that during voltage-induced closure and opening the system explores different regions of the complex free energy landscape, and, in the opening branch, follows quasi-equilibrium paths. III. Physical theory of transport This year we concentrated on the problems of (i) bulk-mediated surface diffusion and (ii) biased diffusion in three-dimensional comb-like structures. Bulk-mediated surface diffusion is attracting a lot of attention in both theory and experiment due to its well-recognized relevance to a wide variety of processes in nature and technology. This kind of diffusion characterizes the motion of particles on a surface that is in a contact with the bulk in a way that allows for the dynamic partitioning of the particles between the surface-bound and bulk states. As a result, particles intermittently diffuse on the surface and in the bulk, allowing for an accelerated propagation of the particles over the surface when bulk diffusivity is significantly larger than its surface counterpart. In particular, our motivation stems from our recent studies of the interaction between certain cytosolic proteins and their membrane embedded targets, which demonstrated that it involves bulk-mediated diffusion over the membrane surface as an essential step. We have developed a new approach to the problem, which reduces its solution to that of a two-state problem of the particle transitions between the surface and the bulk layer, focusing on the cumulative residence times spent by the particle in the two states. These times are random variables, the sum of which is equal to the total observation time. The advantage of the proposed approach is that it allows for a simple exact analytical solution for the double Laplace transform of the conditional probability density of the cumulative residence time spent on the surface by the particle for the observation time. The solution was used to find the Laplace transform of the particle mean square displacement and to analyze the peculiarities of its time behavior over the entire range of time. In the case of biased diffusion in three-dimensional comb-like structures, we developed a formalism that allowed us to derive analytical expressions for the Laplace transforms of the first two moments of the particle displacement along the main tube axis. Through these one can find the time dependencies of the two moments for arbitrary values of both the drift velocity and the dead-end length, including the limiting case of infinitely long dead ends, where the unbiased diffusion becomes anomalous at sufficiently long times. These results give us a set of rigorous tools for quantitative analysis of experimental findings.